1. Field of the Invention
The present invention relates to measurement methods and measurement apparatuses.
2. Description of the Related Art
Innovations in optical systems are brought about by introducing new optical elements or degrees of freedom. For example, improving (enhancing) optical performance by introducing aspheric surfaces is one item that has long been pursued. In recent years, along with advancements in processing technologies and measurement technologies, aspheric surfaces have started to be introduced into exposure apparatuses for semiconductor device manufacturing, which demands the greatest precision. Broadly divided there have been three effects of introducing aspheric surfaces into exposure apparatuses.
A first effect is a reduction in the number of optical elements. In recent years there has been increasing use of short wavelengths in an exposure light and it has been necessary to use high cost glass materials such as quartz and fluorite in optical systems for exposure apparatuses. Accordingly, the reduction in the number of optical elements due to the introduction of aspheric surfaces has advantages in aspects relating to the manufacturing and cost of optical elements.
A second effect is the miniaturization (increasing compactness) of optical systems. Miniaturization of optical systems has become possible by introducing aspheric surfaces, and therefore the influence with respect to aspects relating to the manufacturing and cost of optical systems has been to an extent that cannot be ignored.
A third effect is increasingly high performance of optical systems. A role fulfilled by aspheric surfaces is extremely important in achieving higher optical performance that is increasingly being called for in terms of higher numerical apertures (NA) and lower aberration.
On the other hand, for exposure apparatuses to support rapidly promoting miniaturization of semiconductor devices, consideration is being given to using extreme ultra violet (EUV) rays having a wavelength of approximately 10 nm to 15 nm as an exposure light. Since no glass material (transmissive material) exists through which light transmits in the wavelength range of EUV rays, the optical system must be configured using only mirrors (reflective members) without using lenses. However, reflective materials are also limited for the wavelength range of EUV rays and the reflectivity per single mirror is approximately 70%. Accordingly, since an optical system that satisfies desired optical performance must be configured using as few mirrors as possible, high precision processing and measuring of optical elements (mirrors) having a predetermined aspheric surface figure have become essential technologies. Furthermore, a large aperture optical element (for example, a concave mirror or the like having an effective diameter of 560 mm) is necessary to preserve a highly precise resolution while maintaining an appropriate exposure range using a small number of mirrors.
Thus, a technique for measuring a surface figure of an optical element using an interferometer is proposed in the specification of U.S. Pat. No. 6,781,700. In the specification of U.S. Pat. No. 6,781,700, a surface to be tested having a rotationally symmetric figure is illuminated using light beams that form spherical waves, and this surface to be tested is scanned while being driven in an optical axis direction, thereby obtaining an aspheric surface figure from a drive amount v of the surface to be tested and an optical path length difference p between a position at which the interference patterns become null in a zonal manner and a paraxial center position. Furthermore, based on the drive amount v, a position on the surface to be tested (a position from the aspheric surface axis) h is obtained by solving expression 1 below. Here, null refers to a state in which a density of interference patterns is low.vm(h)=z(h)−R0+h/z′(h)  (Expression 1)
However, z(h) is a design formula that expresses an aspheric surface figure, z′(h) is a value obtained by differentiating z(h) with respect to h, R0 is a paraxial curvature radius, and vm is a measured value of v.
Furthermore, technologies that give attention to measuring abscissas, which are positional information of the surface to be tested, are proposed in Japanese Patent Laid-Open No. 4-48201, Japanese Patent Laid-Open No. 2000-97663, and the specification of US2007/0201035. In Japanese Patent Laid-Open No. 4-48201, Japanese Patent Laid-Open No. 2000-97663, and the specification of US2007/0201035, a relationship between a surface to be tested and an image sensor of an interferometer is obtained based on a difference between a measured result of a state in which the surface to be tested and the reference surface are aligned (alignment state) and a measured result of a state shifted from the alignment state (nonalignment state).
However, with these conventional technologies, there is a limit to the measurement precision for aspheric surfaces (particularly large aperture aspheric surfaces), and highly precise measurements and processing cannot be achieved for aspheric surfaces having an aspheric surface amount that is at least a predetermined value. As is well known, measurement and processing are inseparable, and it is impossible to carry out precise processing without highly precise measurements. In particular, in the cycles of measurement and processing, in addition to performing highly precise measurements of displacement from the design value in a normal line direction of the surface to be tested, it is necessary to perform highly precise measurements of the abscissa, which is positional information on the surface to be tested.
For example, in the specification of U.S. Pat. No. 6,781,700, depending on the aspheric surface, there are cases where the drive amount v in the optical axis direction exceeds 100 mm, and it is extremely difficult to perform highly precise measurements of such a large drive amount v. Furthermore, when obtaining a position h on the surface to be tested from the drive amount v, it is assumed that all the points in a zone indicate information from positions at which lengths from the optical axis of the surface to be tested are equivalent (hereinafter referred to as equivalent radial positions). However, in a case where there is error in the spherical waves that illuminate the surface to be tested, or a case where there is distortion or the like in the optical system of the interferometer, the regions where the interference patterns become null are not necessarily limited to those according to reflected light from the equivalent radial positions on the surface to be tested, and therefore error is produced in measurements of positions on the surface to be tested.
Furthermore, in Japanese Patent Laid-Open No. 4-48201 and Japanese Patent Laid-Open No. 2000-97663, although information is necessary of the entire surface to be tested in the alignment state and the nonalignment state, no specific measurement method is disclosed in regard to aspheric surfaces. It should be noted that in the specification of US2007/0201035, although information of the entire surface to be tested is not absolutely necessary, no specific measurement method is disclosed in regard to aspheric surfaces.